Finite Group Databasebeta

← C2×#23776232 #35168039

Subgroups — C2×#23776232 #35168039

Order 20224.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099285C211yesmaximal, characteristic, complemented
2C2×#19099270C211yesmaximal, characteristic, complemented
3#23776232C2116yesmaximal, direct product factor
4C2×#19098930C211yesmaximal, characteristic, complemented
5C2×#19098923C211yesmaximal, characteristic, complemented
6C2×#19098919C211yesmaximal, characteristic, complemented
7C2×#19098869C211yesmaximal, characteristic, complemented
8C2×#19098848C211yesmaximal, characteristic, complemented
9C2×#19098866C211yesmaximal, characteristic, complemented
10C2×#19098780C211yesmaximal, characteristic
11C2×#19098778C211yesmaximal, characteristic
12C2×#19098766C211yesmaximal, characteristic, complemented
13C2×#19098691C211yesmaximal, characteristic, complemented
14C2×#19098672C211yesmaximal, characteristic
15C2×#19098654C211yesmaximal, characteristic, complemented
16C2×#440×C79C211yesmaximal, characteristic, complemented
17C22×#11929612C2211yescharacteristic
18C22×#11929609C2211yescharacteristic
19#19099285—24no—
20#19099285C2218yescomplemented
21#19099270—24no—
22#19099270C2218yescomplemented
23C2×#14579161C2211yescharacteristic
24C2×#14579159C2211yescharacteristic
25C2×#14579156—21no—
26C2×#14579155—21no—
27C2×#14579152C2211yescharacteristic
28C2×#14579152C2211yescharacteristic
29C2×#14579150C2211yescharacteristic
30C2×#14579149C2211yescharacteristic
31C2×#14579140—21no—
32C2×#14579139—21no—
33C2×#14579138—21no—
34C2×#14579138—21no—
35C2×C4×Dic158C2211yescharacteristic
36C2×#14579126C2211yescharacteristic
37C2×D4×Dic79C2211yescharacteristic
38C2×D4×Dic79C2211yescharacteristic
39C2×#14579123C2211yescharacteristic
40C2×#14579118—21no—
41C22×C4⋊Dic79—21no—
42#19098930C2218yescomplemented
43#19098923C2218yescomplemented
44#19098919C2218yescomplemented
45#19098869C2218yescomplemented
46#19098866C2218yescomplemented
47#19098848C2218yescomplemented
48#19098780C2218yes—
49#19098778C2218yes—
50#19098766C2218yescomplemented
51#19098691C2218yescomplemented
52#19098672C2218yes—
53#19098654C2218yescomplemented
54C2×#14579092C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×C4⋊(C79⋊C8)C2211yescharacteristic
57C2×Dic79⋊C8C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579083C2211yescharacteristic
65C2×#14579083C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#440×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158D411yescharacteristic
79C22×Dic158C2311yescharacteristic
80C22×D316C2311yescharacteristic
81C23×Dic79—21no—
82C23×Dic79—21no—
83C22×C4×D79—21no—
84C2×#11929612—24no—
85C2×#11929612C2314yes—
86C2×#11929609—24no—
87C2×#11929609C2314yes—
88C22×C79⋊C8C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90#14579161—22no—
91#14579161C2314yes—
92#14579159—22no—
93#14579159C2314yes—
94#14579156—28no—
95#14579155—28no—
96#14579152—22no—
97#14579152—22no—
98#14579152C2314yes—
99#14579152C2314yes—
100#14579150—22no—
101#14579150C2314yes—
102#14579149—22no—
103#14579149C2314yes—
104#14579140—28no—
105#14579139—28no—
106#14579138—28no—
107#14579138—28no—
108C4×Dic158D414yes—
109C4×Dic158C2314yes—
110#14579126—22no—
111#14579126C2314yes—
112D4×Dic79—22no—
113D4×Dic79—22no—
114D4×Dic79C2314yes—
115D4×Dic79C2314yes—
116#14579123—22no—
117#14579123C2314yes—
118#14579118—28no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—28no—
123C2×C4⋊Dic79D411yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142C2×C4×Dic79C2311yescharacteristic
143#14579092C2314yes—
144#14579092C2314yes—
145C4⋊(C79⋊C8)C2314yes—
146Dic79⋊C8C2314yes—
147Dic79⋊C8C2314yes—
148#14579086C2314yes—
149#14579086C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579084C2314yes—
153#14579083C2314yes—
154#14579083C2314yes—
155#14579081C2314yes—
156#14579071C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79C2311yescharacteristic
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79—21no—
161C2×SD16×C79—24no—
162C2×SD16×C79C2314yes—
163C22×C8×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C4×Q8×C79—22no—
166C4×Q8×C79C2314yes—
167C4×D4×C79—22no—
168C4×D4×C79C2314yes—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C42×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#107×C79C2314yes—
176#103×C79C2314yes—
177#102×C79C2314yes—
178#97×C79C2314yes—
179C23×D79—21no—
180C2×Dic158—21no—
181C2×Dic158—24no—
182C2×Dic158—22no—
183C2×Dic158—22no—
184C2×Dic158—42no—
185C2×Dic158—82no—
186C2×Dic158C2×D414yes—
187C2×Dic158C2412yes—
188C2×D316—21no—
189C2×D316—22no—
190C2×D316—22no—
191C2×D316C2412yes—
192C22×Dic79—24no—
193C22×Dic79—24no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—82no—
198C22×Dic79—82no—
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C22×Dic79C2×D411yescharacteristic
203C2×C4×D79—24no—
204C2×C4×D79—44no—
205#11929612—28no—
206#11929609—28no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8—22no—
209C2×C79⋊C8C2412yes—
210C2×C79⋊C8C2412yes—
211C4⋊Dic79—24no—
212C4⋊Dic79—24no—
213C4⋊Dic79—24no—
214C4⋊Dic79—21no—
215C4⋊Dic79—21no—
216C4⋊Dic79C2×D414yes—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4C2×D414yes—
225Dic79⋊C4C2×D414yes—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233C4×Dic79—24no—
234C4×Dic79C2×D412yes—
235C4×Dic79C2×D412yes—
236C4×Dic79C2412yes—
237C4×Dic79C2412yes—
238C24×C79—21no—
239C2×Q8×C79—21no—
240C2×Q8×C79—22no—
241C2×Q8×C79—22no—
242C2×Q8×C79C2412yes—
243C2×D4×C79—21no—
244C2×D4×C79—22no—
245C2×D4×C79#4114yes—
246C2×D4×C79C2412yes—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—24no—
251C22×C4×C79—44no—
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2411yescharacteristic
255SD16×C79—28no—
256C2×C8×C79—22no—
257C2×C8×C79—22no—
258C2×C8×C79C2412yes—
259C2×C8×C79C2412yes—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C22⋊C4×C79—24no—
266C42×C79—24no—
267C42×C79C2×D412yes—
268C42×C79C2412yes—
269C23×C79—24no—
270C23×C79—22no—
271C23×C79—42no—
272C23×C79—42no—
273C23×C79C22×D411yescharacteristic
274C22×D79—22no—
275C22×D79—42no—
276C22×D79—42no—
277C22×D79—42no—
278Q8×C79—22no—
279Q8×C79—22no—
280Q8×C79—42no—
281D4×C79—24no—
282D4×C79—22no—
283D4×C79C2×#4114yes—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—48no—
290C2×C4×C79—42no—
291C2×C4×C79—42no—
292C2×C4×C79—42no—
293C2×C4×C79C22×D412yes—
294C2×C4×C79C22×D412yes—
295C2×C4×C79C22×D411yescharacteristic
296C2×C4×C79C2×#4112yes—
297C2×C4×C792−1+412yes—
298C2×C4×C79C2511yescharacteristic
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—42no—
307C2×Dic79—42no—
308C2×Dic79—42no—
309C2×Dic79—84no—
310C2×Dic79—84no—
311C2×Dic79C22×D412yes—
312C2×Dic79C22×D412yes—
313C2×Dic79C22×D412yes—
314C2×Dic79C22×D412yes—
315D316—22no—
316D316—22no—
317D316—42no—
318C4×D79—48no—
319Dic158—22no—
320Dic158—22no—
321Dic158—44no—
322Dic158—42no—
323Dic158—84no—
324C8×C79—22no—
325C8×C79—22no—
326C79⋊C8—22no—
327C79⋊C8—22no—
328C22×C79—24no—
329C22×C79—48no—
330C22×C79—42no—
331C22×C79—42no—
332C22×C79#54812yes—
333C22×C79#57512yes—
334C22×C79#57712yes—
335C22×C79C23×D411yescharacteristic
336C2×D79—42no—
337C2×D79—42no—
338C2×D79—42no—
339C2×D79—84no—
340C4×C79—22no—
341C4×C79—22no—
342C4×C79—42no—
343C4×C79—42no—
344C4×C79—42no—
345C4×C79#54812yes—
346C4×C79C22×#4111yescharacteristic
347C4×C79C2×2−1+411yescharacteristic
348Dic79—22no—
349Dic79—22no—
350Dic79—22no—
351Dic79—22no—
352Dic79—42no—
353Dic79—42no—
354Dic79—42no—
355C2×#3376—791nomaximal, Sylow
356C2×C79—44no—
357C2×C79#337614yescomplemented
358C2×C79C2×#54811yescharacteristic
359C2×C79C2×#57511yescharacteristic
360C2×C79C2×#57711yescharacteristic
361D79—82no—
362C2×#556—791no—
363C2×#554—791no—
364#3376—7916no—
365C2×#491—791no—
366C2×#489—791no—
367C2×#488—791no—
368C2×#479—791no—
369C2×#475—791no—
370C2×#478—791no—
371C2×#463—791no—
372C2×#463—791no—
373C2×#461—791no—
374C2×#446—791no—
375C2×#442—791no—
376C2×#440D7911yescharacteristic, complemented
377C2×C4×SD16—791no—
378C79C2×#337611yescharacteristic, complemented, Sylow
379C22×SD16—791no—
380C22×SD16C2×D7911yescharacteristic
381C22×D8—791no—
382#556—798no—
383#556—1584no—
384#554—798no—
385#554—1584no—
386C2×C4⋊Q8—791no—
387C2×C4⋊Q8—791no—
388C2×#126—1581no—
389C2×#126—1581no—
390C2×#125—791no—
391C2×#125—791no—
392C2×#124—791no—
393C2×#124—791no—
394C2×C22⋊Q8—1581no—
395C2×C22⋊Q8—1581no—
396C2×C22⋊Q8—1581no—
397C2×C22⋊Q8—1581no—
398C2×C4×Q8—791no—
399C2×C4×Q8—791no—
400C2×C4×Q8C2×D7911yescharacteristic
401C2×C4×D4—791no—
402C2×C4×D4—791no—
403C2×C4×D4—791no—
404C2×C4×D4C2×D7911yescharacteristic
405C2×#117—1581no—
406C22×C4⋊C4—1581no—
407#491—798no—
408#489—798no—
409#488—798no—
410#479—798no—
411#478—798no—
412#475—798no—
413#463—798no—
414#463—798no—
415#461—798no—
416#446—798no—
417#442—798no—
418#440C2×D7918yescomplemented
419C4×SD16—798no—
420C2×#107C2×D7911yescharacteristic
421C2×#106—791no—
422C2×#106—791no—
423C2×C4⋊C8—791no—
424C2×C4⋊C8—791no—
425C2×C4⋊C8—791no—
426C2×#103—791no—
427C2×#103—791no—
428C2×#103—791no—
429C2×#103—791no—
430C2×#103—791no—
431C2×#103C2×D7911yescharacteristic
432C2×#102—791no—
433C2×#102—791no—
434C2×#102—791no—
435C2×#102C2×D7911yescharacteristic
436C2×#97—791no—
437C2×#97C2×D7911yescharacteristic
438C2×C4×C8—791no—
439C22×Q8—791no—
440C22×Q8—791no—
441C22×Q8—1581no—
442C22×Q8C22×D7911yescharacteristic
443C22×D4—791no—
444C22×D4C22×D7911yescharacteristic
445C23×C4—21no—
446C23×C4—1581no—
447C23×C4—1581no—
448C23×C4—1581no—
449C2×SD16—24no—
450C2×SD16—794no—
451C2×SD16—1584no—
452C2×SD16C22×D7914yes—
453C2×D8—794no—
454C2×D8—1584no—
455C22×C8—791no—
456C22×C8—791no—
457C22×C8C22×D7911yescharacteristic
458C22×C8C22×D7911yescharacteristic
459C4⋊Q8—794no—
460C4⋊Q8—794no—
461C4⋊Q8—1582no—
462C4⋊Q8—1582no—
463#126—1588no—
464#126—1588no—
465#125—794no—
466#125—794no—
467#125—1582no—
468#125—1582no—
469#124—794no—
470#124—794no—
471#124—1582no—
472#124—1582no—
473C22⋊Q8—1588no—
474C22⋊Q8—1588no—
475C22⋊Q8—1588no—
476C22⋊Q8—1588no—
477C4×Q8—22no—
478C4×Q8—794no—
479C4×Q8—794no—
480C4×Q8—794no—
481C4×Q8—1582no—
482C4×Q8C22×D7914yes—
483C4×D4—22no—
484C4×D4—794no—
485C4×D4—794no—
486C4×D4—794no—
487C4×D4—1582no—
488C4×D4—1582no—
489C4×D4—1582no—
490C4×D4C22×D7914yes—
491#117—1588no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—791no—
494C2×C4⋊C4—791no—
495C2×C4⋊C4—791no—
496C2×C4⋊C4—791no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—1588no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4C22×D7911yescharacteristic
508C2×C4⋊C4C22×D7911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1581no—
511C2×C22⋊C4—1581no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C22⋊C4—1581no—
515C2×C22⋊C4—1581no—
516C2×C22⋊C4—1581no—
517C2×C42—21no—
518C2×C42—791no—
519C2×C42—791no—
520C2×C42—1581no—
521C2×C42C22×D7911yescharacteristic
522#107C22×D7914yes—
523#106—794no—
524#106—794no—
525C4⋊C8—794no—
526C4⋊C8—794no—
527C4⋊C8—794no—
528#103—794no—
529#103—794no—
530#103—794no—
531#103—794no—
532#103—794no—
533#103C22×D7914yes—
534#102—794no—
535#102—794no—
536#102—794no—
537#102C22×D7914yes—
538#97—794no—
539#97C22×D7914yes—
540C4×C8—794no—
541C24—21no—
542C24—1581no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—3162no—
547C2×Q8—794no—
548C2×Q8—792no—
549C2×Q8—6322no—
550C2×Q8—1582no—
551C2×Q8—1582no—
552C2×Q8—1581no—
553C2×Q8—1584no—
554C2×Q8C23×D7912yes—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—792no—
558C2×D4—1582no—
559C2×D4—1582no—
560C2×D4—1581no—
561C2×D4#1192962414yes—
562C2×D4C23×D7912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—44no—
568C22×C4—3164no—
569C22×C4—791no—
570C22×C4—791no—
571C22×C4—791no—
572C22×C4—791no—
573C22×C4—6322no—
574C22×C4—6322no—
575C22×C4—1584no—
576C22×C4—1581no—
577C22×C4—1581no—
578C22×C4—1581no—
579C22×C4—1584no—
580C22×C4—1584no—
581C22×C4D4×D7911yescharacteristic
582C22×C4D4×D7911yescharacteristic
583C22×C4C23×D7911yescharacteristic
584SD16—28no—
585SD16—1588no—
586D8—1588no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—792no—
590C2×C8—792no—
591C2×C8—1582no—
592C2×C8—1582no—
593C2×C8C23×D7912yes—
594C2×C8C23×D7912yes—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—794no—
599C4⋊C4—794no—
600C4⋊C4—794no—
601C4⋊C4—792no—
602C4⋊C4—792no—
603C4⋊C4—1584no—
604C4⋊C4—1584no—
605C4⋊C4—1584no—
606C4⋊C4—1584no—
607C4⋊C4—1584no—
608C4⋊C4—1584no—
609C4⋊C4—1584no—
610C4⋊C4—1581no—
611C4⋊C4—1581no—
612C4⋊C4—1584no—
613C4⋊C4C23×D7912yes—
614C4⋊C4C23×D7912yes—
615C22⋊C4—24no—
616C22⋊C4—1584no—
617C22⋊C4—1584no—
618C22⋊C4—1584no—
619C22⋊C4—1584no—
620C22⋊C4—1584no—
621C22⋊C4—1584no—
622C22⋊C4—1584no—
623C42—24no—
624C42—792no—
625C42—792no—
626C42—792no—
627C42—792no—
628C42—1584no—
629C42D4×D7912yes—
630C42C23×D7912yes—
631C23—24no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—3162no—
636C23—3162no—
637C23—3162no—
638C23—1582no—
639C23C2×D4×D7911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—3164no—
644Q8—3162no—
645Q8—6324no—
646Q8—1582no—
647Q8—1582no—
648D4—22no—
649D4—24no—
650D4—3162no—
651D4—1582no—
652D4—1582no—
653D4C2×#1192962414yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—48no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—3168no—
664C2×C4—3162no—
665C2×C4—3162no—
666C2×C4—3162no—
667C2×C4—792no—
668C2×C4—792no—
669C2×C4—792no—
670C2×C4—792no—
671C2×C4—6324no—
672C2×C4—6324no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1582no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4C2×D4×D7912yes—
681C2×C4C2×D4×D7912yes—
682C2×C4C2×D4×D7911yescharacteristic
683C2×C4C2×#1192962412yes—
684C2×C4#1457920812yes—
685C2×C4C24×D7911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1582no—
689C8—1582no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—3162no—
695C22—3162no—
696C22—3162no—
697C22—6324no—
698C22#1909922212yes—
699C22#1909935912yes—
700C22#1909937212yes—
701C22C22×D4×D7911yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—3162no—
708C4—3162no—
709C4—3162no—
710C4—1582no—
711C4—1582no—
712C4—1582no—
713C4—1582no—
714C4#1909922212yes—
715C4C22×#1192962411yescharacteristic
716C4C2×#1457920811yescharacteristic
717C2—44no—
718C2—6322no—
719C2#2377623214yesdirect product factor
720C2C2×#1909922211yescharacteristic
721C2C2×#1909935911yescharacteristic
722C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#440×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929609C22
hypercenterC2×#440D79
hypocenterC79C2×#3376
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19099285C2semidirect
2. C2×#19099270C2semidirect
3. #23776232C2direct (N × H)
4. C2×#19098930C2semidirect
5. C2×#19098923C2semidirect
6. C2×#19098919C2semidirect
7. C2×#19098869C2semidirect
8. C2×#19098848C2semidirect
9. C2×#19098866C2semidirect
12. C2×#19098766C2semidirect
13. C2×#19098691C2semidirect
15. C2×#19098654C2semidirect
16. C2×#440×C79C2semidirect
20. #19099285C22semidirect
22. #19099270C22semidirect
42. #19098930C22semidirect
43. #19098923C22semidirect
44. #19098919C22semidirect
45. #19098869C22semidirect
46. #19098866C22semidirect
47. #19098848C22semidirect
50. #19098766C22semidirect
51. #19098691C22semidirect
53. #19098654C22semidirect
72. #440×C79C22semidirect
357. C2×C79#3376semidirect
376. C2×#440D79semidirect
378. C79C2×#3376semidirect
418. #440C2×D79semidirect
719. C2#23776232direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#190992852
C2×#190992702
#237762322
C2×#190989302
C2×#190989232
C2×#190989192
C2×#190988692
C2×#190988482
C2×#190988662
C2×#190987802
C2×#190987782
C2×#190987662
C2×#190986912
C2×#190986722
C2×#190986542
C2×#440×C792
C2×#337679